Tutorial 11                                     Erindale: Thu@3pm  970403
===========                                    St George: Thu@6pm

CSC354, Spring 1997                                   Tutorial notes, T11
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Announce:
  - ps3 due today

Topics:
  - simple queueing theory questions.  Tutorial will be
      based on lecture material in Chapter 7, with an
      emphasis on Sections 7.5 and 7.6.

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Here is the example that will be covered in tutorial:

SimCorp is planning a country-wide chain of small kiosks, selling
simulated hamburgers, called VR burgers. Each kiosk will be staffed
by 2 persons, but how customers place their orders and are served
still needs to be worked out.

Plan A
Customers get in a single line at the counter, with both attendants
working together to fill the order of the first customer in line.
Call this the Twice-as-Fast (TAF) system.

Plan B
There should be a separate line for each cash register, with rails
to keep customers from jumping lines. A worker would take the order,
prepare the food, and then accept payment. Customers would have a
50:50 chance of getting into either line. Call this the Random-Line
(RL) system.

Plan C
Take plan B and transform it into one where customers choose the
shorter line upon arrival to the kiosk. Call this the Shorter-Line
(SL) system.

Plan D
Make room for one waiting line, but separate cash registers.
Customers wait in line until one of the attendants is free and
then step up to that register for full service. Call this the
Common-Line (CL) system.

Here are the common parameters:
- the average time for one worker to perform either job (register or grill)
    is 1 minute; taking the order is 0 time
- the average time for one worker to perform both jobs is 2 minutes
- the average time for both workers to perform both jobs for one
    customer is 1 minute
- when there are less than 3 customers in the kiosk system (waiting +
    service), new customers arrive at an average rate of 1 every 2 minutes;
    otherwise, the arrival rate is 0
- exponential assumptions are warranted

For each of the plans:
I. Draw the queueing pictures (queue(s) and server(s) and routing and
parameters) to show the structure of the model.
II. Draw the state transition rate diagram (states and transitions and
labels).

Do not bother solving the resulting equations. If there is time, the
TAs will discuss the performance numbers that come from the analysis.
But your job here is to form the model and derive the basis for the
steady-state evaluation.

bfn